Consider the function f(x) = min\ |x^ 2 - 9|, |x^ 2 - 1|\ , then...

Consider the function

f\left(x\right) = min\left\{ \left|x^{2} - 9\right|, \left|x^{2} - 1\right|\right\}

then the number of points where f\left(x\right)

is non-differentiable is/are $Consider the function f(x) = min\ |x^ 2 - 9|, |x^ 2 - 1|\ , then the number of points where f(x) is non-differentiable$

Options

A $0$
B $7$
C $6$
D $4$

Correct answer

C. $6$

Step-by-step solution

Using the graph of

y = \left|x^{2} - 9\right|, y = \left|x^{2} - 1\right|

$Consider the function f(x) = min\ |x^ 2 - 9|, |x^ 2 - 1|\ , then the number of points where f(x) is non-differentiable$
Clearly, from the graph,
we can see that

f ( x )

is non-differentiable at

6

points

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